Add smallest_moved_point and largest_moved_point

docs/src/Groups/permgroup.md

@@ -109,6 +109,13 @@ julia> x(6)
 6
 ```
 
+## Moved points of permutations and permutation groups
+```@docs
+smallest_moved_point
+largest_moved_point
+moved_points
+number_of_moved_points
+```
 
 ## Cycle structures
 

src/GAP/wrappers.jl

@@ -379,6 +379,7 @@ GAP.@wrap SizeOfFieldOfDefinition(x::GapObj, y::GapInt)::GapInt
 GAP.@wrap SizesCentralizers(x::GapObj)::GapObj
 GAP.@wrap SizesConjugacyClasses(x::GapObj)::GapObj
 GAP.@wrap SLPforElement(x::GapObj, y::GapObj)::GAP.Obj
+GAP.@wrap SmallestMovedPoint(x::Any)::GapInt
 GAP.@wrap Source(x::GapObj)::GapObj
 GAP.@wrap Sqrt(x::Int64)::GAP.Obj
 GAP.@wrap Stabilizer(v::GapObj, w::Any, x::GapObj, y::GapObj, z::GapObj)::GapObj

src/Groups/perm.jl

@@ -84,6 +84,63 @@ function (G::PermGroup)(H::PermGroup)
   throw(ArgumentError("H has degree $dH, cannot be coerced to degree $dG"))
 end
 
+@doc raw"""
+    smallest_moved_point(x::PermGroupElem) -> Union{Int, PosInf}
+
+Return the smallest positive integer which is not fixed by `x` if
+such an integer exists, and `inf` if `x` is the identity.
+
+    smallest_moved_point(G::PermGroup) -> Union{Int, PosInf}
+
+Return the smallest positive integer which is not fixed by `G` if
+such an integer exists, and `inf` if `G` is trivial.
+
+# Examples
+```jldoctest
+julia> g = symmetric_group(4);  s = sylow_subgroup(g, 3)[1];
+
+julia> smallest_moved_point(s)
+1
+
+julia> smallest_moved_point(gen(s, 1))
+1
+
+julia> smallest_moved_point(one(s))
+infinity
+```
+"""
+function smallest_moved_point(x::Union{PermGroupElem,PermGroup})
+  pt = GAPWrap.SmallestMovedPoint(GapObj(x))
+  pt isa Int && return pt
+  return inf
+end
+
+@doc raw"""
+    largest_moved_point(x::PermGroupElem) -> Int
+
+Return the largest positive integer which is not fixed by `x` if
+such an integer exists, and `0` if `x` is the identity.
+
+    largest_moved_point(G::PermGroup) -> Int
+
+Return the largest positive integer which is not fixed by `G` if
+such an integer exists, and `0` if `G` is trivial.
+
+# Examples
+```jldoctest
+julia> g = symmetric_group(4);  s = sylow_subgroup(g, 3)[1];
+
+julia> largest_moved_point(s)
+3
+
+julia> largest_moved_point(gen(s, 1))
+3
+
+julia> largest_moved_point(one(s))
+0
+```
+"""
+largest_moved_point(x::Union{PermGroupElem,PermGroup}) = GAPWrap.LargestMovedPoint(GapObj(x))
 
 @doc raw"""
     moved_points(x::PermGroupElem) -> Vector{Int}

src/exports.jl

@@ -1099,6 +1099,7 @@ export label!
 export labeled_matrix_formatted
 export labelings
 export laplacian_matrix
+export largest_moved_point
 export lattice_homomorphism
 export lattice_of_cyclic_flats
 export lattice_of_flats
@@ -1653,6 +1654,7 @@ export small_generating_set, has_small_generating_set, set_small_generating_set
 export small_group
 export small_group_identification, has_small_group_identification
 export smaller_degree_permutation_representation
+export smallest_moved_point
 export snub_cube
 export snub_dodecahedron
 export socle, has_socle, set_socle